Simplify; express your answer in exponential form. Assume $r\neq 0, t\neq 0$. $\dfrac{{(r^{-1}t)^{5}}}{{(r^{-5}t)^{5}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(r^{-1}t)^{5} = (r^{-1})^{5}(t)^{5}}$ On the left, we have ${r^{-1}}$ to the exponent ${5}$ . Now ${-1 \times 5 = -5}$ , so ${(r^{-1})^{5} = r^{-5}}$ Apply the ideas above to simplify the equation. $\dfrac{{(r^{-1}t)^{5}}}{{(r^{-5}t)^{5}}} = \dfrac{{r^{-5}t^{5}}}{{r^{-25}t^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{-5}t^{5}}}{{r^{-25}t^{5}}} = \dfrac{{r^{-5}}}{{r^{-25}}} \cdot \dfrac{{t^{5}}}{{t^{5}}} = r^{{-5} - {(-25)}} \cdot t^{{5} - {5}} = r^{20}$